Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks.
In this book, various aspects of these stochastic models are investigated in depth in an...
Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general r...
In the 2nd edition some sections of Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.
In the 3rd printing of the 2nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the...
In the 2nd edition some sections of Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. As...
In many complex systems one can distinguish fast and slow processes with radically di?erent velocities. In mathematical models based on di?er- tialequations, suchtwo-scalesystemscanbedescribedbyintroducingexpl- itly a small parameter?on the left-hand side ofstate equationsfor the fast variables, and these equationsare referredto assingularly perturbed. Surpr- ingly, this kind of equation attracted attention relatively recently (the idea of distinguishing fast and slow movements is, apparently, much older). Robert O Malley, in comments to his book, attributes the originof the whole...
In many complex systems one can distinguish fast and slow processes with radically di?erent velocities. In mathematical models based on di?er- tialequ...
Queueing theory is a fascinating subject in Applied Probability for two con- tradictory reasons: it sometimes requires the most sophisticated tools of stochastic processes, and it often leads to simple and explicit answers. More- over its interest has been steadily growing since the pioneering work of Erlang in 1917 on the blocking of telephone calls, to the more recent applications on the design of broadband communication networks and on the performance evaluation of computer architectures. All this led to a huge literature, articles and books, at various levels of mathematical rigor....
Queueing theory is a fascinating subject in Applied Probability for two con- tradictory reasons: it sometimes requires the most sophisticated tools of...
Along with conventional problems of statistics and probability, the - vestigation of problems occurring in what is now referred to as stochastic theory of optimal control also started in the 1940s and 1950s. One of the most advanced aspects of this theory is the theory of optimal stopping rules, the development of which was considerably stimulated by A. Wald, whose Sequential nal sis' was published in 1947. In contrast to the classical methods of mathematical statistics, according to which the number of observations is fixed in advance, the methods of sequential analysis are characterized by...
Along with conventional problems of statistics and probability, the - vestigation of problems occurring in what is now referred to as stochastic theor...
Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks.
In this book, various aspects of these stochastic models are investigated in depth in an...
Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general r...
In many complex systems one can distinguish fast and slow processes with radically di?erent velocities. In mathematical models based on di?er- tialequations, suchtwo-scalesystemscanbedescribedbyintroducingexpl- itly a small parameter?on the left-hand side ofstate equationsfor the fast variables, and these equationsare referredto assingularly perturbed. Surpr- ingly, this kind of equation attracted attention relatively recently (the idea of distinguishing fast and slow movements is, apparently, much older). Robert O Malley, in comments to his book, attributes the originof the whole...
In many complex systems one can distinguish fast and slow processes with radically di?erent velocities. In mathematical models based on di?er- tialequ...
